Fluctuations and initial state granularity in
heavy ion collisions and their effects on
observables from hydrodynamics
R.P.G.Andrade1 , A.L.V.R.dos Reis1 , F.Grassi1 , Y.Hama1 ,
T.Kodama2, W.L.Qian1
1 Instituto
2 Instituto
de Física, Universidade de São Paulo, Brazil
de Física, Universidade Federal do Rio de Janeiro, Brazil
IV WPCF, Krakow 09/2008
Outline
Objective
Summary of the comparison between fluctuating and average IC
Directed flow: what is expected
Results on directed flow at RHIC
What we have learned and what we need to do
Objective
Hydrodynamics has been rather successful at describing
results obtained in relativistic nuclear collisions at RHIC.
Usually, smooth initial conditions are assumed.
For example:
left: T.Hirano Phys.Rev.C65 (2001) 011901R; right: C.Nonaka and S.Bass
Phys.Rev.C75 (2007) 014902.
In reality, one expects that initial conditions event-by-event, are
not smooth.
Here are examples from NeXuS:
η = 0 slice for initial energy density of a RHIC collision in the 6-15% centrality
window
Can such structures (hot spots) have a sizable effect on
variables?
To solve the hydro equations with very irregular initial
conditions, we use the SPheRIO code:
It is based on the method of Smoothed Particle
Hydrodynamics, originally developed in astrophysics and
adapted to relativistic heavy ion collisions
C.E.Aguiar, T.Kodama, T.Osada & Y.Hama, J.Phys.G27(2001)75;
Y.Hama, T.Kodama & O.Socolowski Jr. Braz.J.Phys. 35(2005)24
The version of NeXSPheRIO used here has
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initial conditions provided by NeXus
[H.J. Drescher, F.M. Liu, S. Ostrapchenko, T. Pierog and K. Werner,
Phys.
and normalized by an η-dependent factor to reproduce
dNch /d η in each centrality window
Y.Hama et al. et al. Yad. Fiz. 71 1588 (2008)
I
an eos with a critical point
Y. Hama et al. QM05 proceedings, Nucl.Phys. A774 169 (2006)
I
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incorporating strangeness conservation.
Tf .out is fixed (mostly) by dNch /pt dpt and depends on the
centrality window (i.e. number of participants).
centrality windows are defined as experimentally, using
participant number and not impact paremeter
R.Andrade et al. Braz.J.Phys. 34 319 (2004)
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an ideal fluid.
A code with Smoothed Particle Hydrodynamics +
dissipation is under development
G.S.Denicol, T.Kodama, Ph.Mota
Summary of the comparison between fluctuating and
average initial conditions
pT spectra: the high pt part is lifted
Y.Hama’s talk and R.P.G. Andrade et al., Phys. Rev. Lett. in print
1000
freeze-out temp. = 130.1 MeV
centrality = (6 - 15)%
100
10
-2
0.2 < y < 1.4
-1 2
(2π pt ) d N/dydpt (GeV)
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partic. (225 - 300)
1
Exp. data
freeze-out temp. = 140.0 MeV
centrality = (35 - 45)%
100
10
0.2 < y < 1.4
partic. (80 - 115)
1
Exp. data
0.1
0
0.5
1
pt (GeV)
1.5
2
I
v2 (pt ) is flatter
Y.Hama’s talk, R.P.G. Andrade et al., Phys. Rev. Lett. in print and
Phys.Rev.Lett.97 (2006) 20230
0.2
total centrality = (0 - 50)%
partic. (60 - 394)
v2
0.15
0 < η < 1.5
Exp. data
0.1
partial centr.
(0 - 6)%
(6 - 15)%
(15 - 25)%
(25 - 35)%
(35 - 45)%
(45 - 50)%
0.05
0
0
0.5
1
2
1.5
freeze-out temp. (MeV)
128.1
130.1
133.0
136.3
140.0
143.2
2.5
3
4
3.5
p (GeV)
t
v2 (η) has no shoulder
ref.: see above
0.07
0.06
NexSPheRIO results
(25-50)%
(15-25)%
(3-15)%
0.05
v2
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0.04
0.03
0.02
∆
0.01
-4
-2
Exp. data
0
η
2
4
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HBT
Y.Hama’s talk and O.Socolowski Jr. et al. Phys.Rev.Lett. 93 (2004)
182301
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a ridge may appear
Y.Hama’s talk, preliminary work by J.Takashi and B.Tavares
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directed flow
THIS TALK
Directed flow: what is expected
If a nucleus-nucleus collision
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is a number of independent nucleon-nucleon collisions ⇒
the momentum distribution is isotropic
ρ =dN/d φ
φ
b
x
z
y
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leads to thermalized matter (in overlap region) ⇒ the
momentum distribution is stretched
O
b
y
x
φ
b
A
ρ =dN/d φ
B
z
y
v2 = measure of this stretching, so teaches about IC,
thermalization, etc
x
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There is also the possibility that the momentum distribution
be shifted/deformed towards one of the sides:
v1 = measure of this shift
Directed flow at the SPS
Pions and protons behave oppositely (both at 40A GeV and
158 A GeV):
NA49, Phys.Rev.C 68 (2003) 034903
At some energy, a “wiggle” in v1 is predicted:
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In some microscopical models, for nucleons:
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RQMD at AGS energy: Snellings et al. Phys.Rev.Lett. 84
(2000) 2804
UrQMD at RHIC energy: Bleicher and Stöcker
Phys.Lett.B526 (2002) 309
See also:
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UrQMD at SPS energy: Petersen et al. Phys.Rev. C74
(2006) 064908
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In hydro models, for the fluid, if a QGP phase occurs:
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at AGS energy: Csernai and Röhrich, Phys.Lett.B458
(1999) 454
at AGS energy: Brachmann et al. Phys.Rev.C61 (2000)
024909
See also:
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Rischke et al. Heavy Ion Phys. 1 (1995) 309
Ivanov et al. Acta Phys. Hung. 15 (2002) 117
Results on directed flow at RHIC
General shape from PHOBOS and STAR
v1 (%)
Results are for charged particles (pions dominate) and rather
similar to pions from NA49
0.4
3
0.2
0
2
-0.2
1
-0.4
-1
-0.5
0
0.5
1
0
0 - 5%
5 - 40%
40 - 80%
PHOBOS: 6 - 40%
〈 px 〉 / 〈 p 〉: 0 - 5%
-1
-2
-3
-6
t
-4
-2
0
2
4
6
η
PHOBOS Phys.Rev.Lett.97 (2006) 012301 and STAR Phys.Rev.Lett.92
(2004) 062301; arXiv:0807.1518
NeXSPheRIO results
Qualitative agreement with PHOBOS for all ηs
Quantitative agreement for | η |< 3
As for v2 , large fluctuations are predicted.
Qualitative agreement for | η |< 3 Turnover occurs for smaller η
than for STAR
System-size independence
v1 (%)
Observed by STAR.
0
-0.2
-0.4
v1 (%)
-0.6 |η| < 1.3
0
2.5 < |η| < 4
-2
-4
-6
-8
0
200 GeV Au+Au
200 GeV Cu+Cu
62.4 GeV Au+Au
62.4 GeV Cu+Cu
10 20
30 40 50 60 70
80
% Most Central
v1 (η) from NeXSpheRIO for various centrality windows for
Au+Au and Cu+Cu at 200 A GeV (PRELIMIMARY)
Little dependence on A in the windows 6-15% to 45-55%.
Statistics must be improved.
Particle type dependence
In NeXSPheRIO (left), protons have a big wiggle, pions much
less, as seen in microscopic codes such as UrQMD (right).
PRELIMINARY
Preliminary results for identified particles around y = 0 available from STAR
J.Phys.G35 (2008) 044072
In NeXSPheRIO (left), antiprotons behave opposite to protons,
as seen with UrQMD (right). PRELIMINARY
Equation of state dependence
v1 for equation of state with critical point or with a phase
transition are similar (PRELIMINARY):
Effect of granularity
v1 has a plateau for fluctuationg initial conditions and a
somewhat stronger negative inclination for smooth initial
conditions (PRELIMINARY):
What we have learned and what we need to do
I
v1 (η) for pions has a plateau around η = 0. Nucleons
seem to have a wiggle.
Qualitative agreement with data for charged particles.
I
v1 (η) seems rather independent of the system-size.
Why?
(For a given energy, the tilt of the ellipsoid in the x-z plane
is weakly A-dependent?)
I
v1 (η) is similar for an equation of state with critical point or
with a phase transition. Is it because it is generated very
early, in both cases in a QGP?
I
v1 (η) seems attenuated when using fluctuating IC rather
than with smooth IC.
What is the relation with the hot spots?
I
We need to understand the origin of directed flow in our
code to get a more clear picture.
What we have learned and what we need to do
I
v1 (η) for pions has a plateau around η = 0. Nucleons
seem to have a wiggle.
Qualitative agreement with data for charged particles.
I
v1 (η) seems rather independent of the system-size.
Why?
(For a given energy, the tilt of the ellipsoid in the x-z plane
is weakly A-dependent?)
I
v1 (η) is similar for an equation of state with critical point or
with a phase transition. Is it because it is generated very
early, in both cases in a QGP?
I
v1 (η) seems attenuated when using fluctuating IC rather
than with smooth IC.
What is the relation with the hot spots?
I
We need to understand the origin of directed flow in our
code to get a more clear picture.
What we have learned and what we need to do
I
v1 (η) for pions has a plateau around η = 0. Nucleons
seem to have a wiggle.
Qualitative agreement with data for charged particles.
I
v1 (η) seems rather independent of the system-size.
Why?
(For a given energy, the tilt of the ellipsoid in the x-z plane
is weakly A-dependent?)
I
v1 (η) is similar for an equation of state with critical point or
with a phase transition. Is it because it is generated very
early, in both cases in a QGP?
I
v1 (η) seems attenuated when using fluctuating IC rather
than with smooth IC.
What is the relation with the hot spots?
I
We need to understand the origin of directed flow in our
code to get a more clear picture.
What we have learned and what we need to do
I
v1 (η) for pions has a plateau around η = 0. Nucleons
seem to have a wiggle.
Qualitative agreement with data for charged particles.
I
v1 (η) seems rather independent of the system-size.
Why?
(For a given energy, the tilt of the ellipsoid in the x-z plane
is weakly A-dependent?)
I
v1 (η) is similar for an equation of state with critical point or
with a phase transition. Is it because it is generated very
early, in both cases in a QGP?
I
v1 (η) seems attenuated when using fluctuating IC rather
than with smooth IC.
What is the relation with the hot spots?
I
We need to understand the origin of directed flow in our
code to get a more clear picture.
What we have learned and what we need to do
I
v1 (η) for pions has a plateau around η = 0. Nucleons
seem to have a wiggle.
Qualitative agreement with data for charged particles.
I
v1 (η) seems rather independent of the system-size.
Why?
(For a given energy, the tilt of the ellipsoid in the x-z plane
is weakly A-dependent?)
I
v1 (η) is similar for an equation of state with critical point or
with a phase transition. Is it because it is generated very
early, in both cases in a QGP?
I
v1 (η) seems attenuated when using fluctuating IC rather
than with smooth IC.
What is the relation with the hot spots?
I
We need to understand the origin of directed flow in our
code to get a more clear picture.
What we have learned and what we need to do
I
v1 (η) for pions has a plateau around η = 0. Nucleons
seem to have a wiggle.
Qualitative agreement with data for charged particles.
I
v1 (η) seems rather independent of the system-size.
Why?
(For a given energy, the tilt of the ellipsoid in the x-z plane
is weakly A-dependent?)
I
v1 (η) is similar for an equation of state with critical point or
with a phase transition. Is it because it is generated very
early, in both cases in a QGP?
I
v1 (η) seems attenuated when using fluctuating IC rather
than with smooth IC.
What is the relation with the hot spots?
I
We need to understand the origin of directed flow in our
code to get a more clear picture.